Electric power is ordinarily delivered to residences, commercial facilities, and industrial facilities as AC (alternating current) voltage that approximates a sine wave with respect to time, and ordinarily flows through a residence or facility as an AC current that also approximates a sine wave with respect to time. The electric power distribution system operates most efficiently and most safely when both the voltage and current are sine waves. However, certain kinds of loads draw current in a non-sinusoidal waveform, and, if, these loads are large relative to the distribution system source impedance, the system voltage can become non-sinusoidal as well.
These non-sinusoidal voltage and current waveforms may be conveniently expressed as a Fourier series (a sum of sinusoidal waveforms of varying frequency, amplitude, and phase angle). Under most circumstances, the Fourier series for AC power system voltage and currents consists of a fundamental frequency, typically 50 Hertz or 60 Hertz, plus integer multiples of the fundamental frequency. These integer multiples of the fundamental frequency are referred to as "harmonics".
Instruments for measuring AC power system voltage and current harmonics are well known to those skilled in the art. One such commercially available instrument is the model A PowerProfiler available from Basic Measuring Instruments, Foster City, Calif. Another commercially available instrument is the Model HP3588A Spectrum Analyzer available from the Hewlett Packard Corporation of Santa Clara, Calif. These instruments provide rapid, accurate assessment of the level of harmonic voltages and currents on an AC power system.
With the growing popularity of non-linear electric power loads such as adjustable speed drives, personal computers, and arc furnaces, it is often desirable to determine and record whether the level of voltage harmonics or current harmonics exceed some limit. As a general rule, the supplier of electricity is responsible for ensuring that the voltage harmonics are below some threshold, and the consumer of electricity is responsible for keeping harmonic currents below some other threshold. Harmonic thresholds are thus used to assign responsibility for eliminating voltage and current harmonics.
Table 1 below represents an example of a desired set of limits on voltage harmonics that apply to the provider of power. The Bus Voltage is measured at the point of common coupling (PCC) and the Total Harmonic Voltage Distortion (THD) is calculated as a percentage of the nominal fundamental frequency voltage.
TABLE 1 ______________________________________ Voltage Distortion Limits Individual Harmonic Total Harmonic Voltage Distortion Voltage Distortion Bus Voltage at PCC (%) THD (%) ______________________________________ Below 69 kV 3.0 5.0 69 kV to 138 kV 1.5 2.5 138 kV and above 1.0 1.5 ______________________________________
Table 2 below represents an example of a desired set of limits on current harmonics that apply to the consumer of power. The Maximum Harmonic Current Distortion as a percentage of the maximum demand load current (I.sub.L) at the fundamental frequency measured at the PCC is presented for odd harmonics in different ranges of the maximum short circuit current (I.sub.SC) measured at the PCC divided by I.sub.L. The column at the far right of the table represents the Total Demand Distortion (TDD) harmonic current distortion as a percentage of the maximum demand load current. The even harmonics are limited to 25% of the odd harmonic limits in the table.
TABLE 2 ______________________________________ Current Distortion Limits Maximum Harmonic Current Distortion in % of I.sub.L Harmonic Order (Odd Harmonics) 11 .ltoreq. 17 .ltoreq. 23 .ltoreq. I.sub.SC /I.sub.L &lt;11 h &lt; 17 h &lt; 23 h &lt; 35 35 .ltoreq. h TDD ______________________________________ &lt;20 4.0 2.0 1.5 0.6 0.3 5.0 20 &lt; 50 7.0 3.5 2.5 1.0 0.5 8.0 50 &lt; 100 10.0 4.5 4.0 1.5 0.7 12.0 100 &lt; 1000 12.0 5.5 5.0 2.0 1.0 15.0 &gt;1000 15.0 7.0 6.0 2.5 1.4 20.0 ______________________________________
Commercially available instruments such as the Basic Measuring Instruments model 3030A can be equipped with a feature that allows a user to program a threshold for a voltage harmonic, and program a second threshold for a current harmonic, then receive an alarm if these thresholds are exceeded. However, these independent thresholds fail to take into account the fact that increased harmonic currents may cause increased harmonic voltages. Consequently, independent voltage and current harmonic thresholds are not optimal for assigning responsibility for harmonic problems.
Commercially available power system harmonic instruments, such as the Basic Measuring Instruments model 3030A and the Model 8000 power Analyzer available from Dranetz Technologies of Edison, N.J., apply each harmonic threshold independently to each phase on poly-phase systems. For example, if the user selects a 4% threshold on the fifth current harmonic, these instruments will sound an alarm if the fifth current harmonic on Phase A of a three phase system exceeds 4%, or if the fifth current harmonic on Phase B of a three phase system exceeds 4%, or if the fifth current harmonic on Phase C of a three phase system exceeds 4%. This method of applying harmonic thresholds fails to accurately assess the physical impact of the harmonic levels on polyphase distribution systems.
Commercially available instruments such as the BMI Model 3030A and the Dranetz Technologies Model 8000 offer the ability to chart harmonic levels over time. This approach is useful for analyzing a harmonic problem; however, it cannot provide a yes or no answer to the question: does this measurement location have a harmonics problem? Simpler instruments, such as the one disclosed by Grassel et al. in U.S. Pat. 4,964,055, offer the ability to take a snapshot of harmonic levels. Although this method can provide a yes or no answer to the question posed above for one instant in time, harmonic levels typically fluctuate widely with time of day, types of loads turned on, and other factors, so it cannot provide an answer over a period of time.
It is an object of this invention to provide a simple, direct indication of whether there is a harmonics problem at a measurement location that takes into account the variation in harmonic levels over time. It is a further object of this invention to apply harmonics thresholds to poly-phase power systems in a way that more accurately reflects the physical impact of harmonics on AC power distribution systems. It is a further object of this invention to apply harmonic thresholds to AC power systems in a way that acknowledges that increased harmonic currents can cause increased harmonic voltages.